Best Known (27−19, 27, s)-Nets in Base 32
(27−19, 27, 98)-Net over F32 — Constructive and digital
Digital (8, 27, 98)-net over F32, using
- t-expansion [i] based on digital (7, 27, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
(27−19, 27, 129)-Net in Base 32 — Constructive
(8, 27, 129)-net in base 32, using
- 1 times m-reduction [i] based on (8, 28, 129)-net in base 32, using
- base change [i] based on digital (0, 20, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 20, 129)-net over F128, using
(27−19, 27, 2978)-Net in Base 32 — Upper bound on s
There is no (8, 27, 2979)-net in base 32, because
- 1 times m-reduction [i] would yield (8, 26, 2979)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1363 797517 591949 686578 634505 126508 045224 > 3226 [i]